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From: olcott <polcott333@gmail.com>
Newsgroups: comp.theory
Subject: Re: Undecidability based on epistemological antinomies V2 --H(D,D)--
Date: Fri, 26 Apr 2024 10:34:14 -0500
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On 4/26/2024 3:32 AM, Mikko wrote:
> On 2024-04-25 14:15:20 +0000, olcott said:
> 
>> On 4/25/2024 3:16 AM, Mikko wrote:
>>> On 2024-04-25 00:17:57 +0000, olcott said:
>>>
>>>> On 4/24/2024 6:01 PM, Richard Damon wrote:
>>>>> On 4/24/24 11:33 AM, olcott wrote:
>>>>>> On 4/24/2024 3:35 AM, Mikko wrote:
>>>>>>> On 2024-04-23 14:31:00 +0000, olcott said:
>>>>>>>
>>>>>>>> On 4/23/2024 3:21 AM, Mikko wrote:
>>>>>>>>> On 2024-04-22 17:37:55 +0000, olcott said:
>>>>>>>>>
>>>>>>>>>> On 4/22/2024 10:27 AM, Mikko wrote:
>>>>>>>>>>> On 2024-04-22 14:10:54 +0000, olcott said:
>>>>>>>>>>>
>>>>>>>>>>>> On 4/22/2024 4:35 AM, Mikko wrote:
>>>>>>>>>>>>> On 2024-04-21 14:44:37 +0000, olcott said:
>>>>>>>>>>>>>
>>>>>>>>>>>>>> On 4/21/2024 2:57 AM, Mikko wrote:
>>>>>>>>>>>>>>> On 2024-04-20 15:20:05 +0000, olcott said:
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> On 4/20/2024 2:54 AM, Mikko wrote:
>>>>>>>>>>>>>>>>> On 2024-04-19 18:04:48 +0000, olcott said:
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>> When we create a three-valued logic system that has these
>>>>>>>>>>>>>>>>>> three values: {True, False, Nonsense}
>>>>>>>>>>>>>>>>>> https://en.wikipedia.org/wiki/Three-valued_logic
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>> Such three valued logic has the problem that a 
>>>>>>>>>>>>>>>>> tautology of the
>>>>>>>>>>>>>>>>> ordinary propositional logic cannot be trusted to be 
>>>>>>>>>>>>>>>>> true. For
>>>>>>>>>>>>>>>>> example, in ordinary logic A ∨ ¬A is always true. This 
>>>>>>>>>>>>>>>>> means that
>>>>>>>>>>>>>>>>> some ordinary proofs of ordinary theorems are no longer 
>>>>>>>>>>>>>>>>> valid and
>>>>>>>>>>>>>>>>> you need to accept the possibility that a theory that 
>>>>>>>>>>>>>>>>> is complete
>>>>>>>>>>>>>>>>> in ordinary logic is incomplete in your logic.
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> I only used three-valued logic as a teaching device. 
>>>>>>>>>>>>>>>> Whenever an
>>>>>>>>>>>>>>>> expression of language has the value of {Nonsense} then 
>>>>>>>>>>>>>>>> it is
>>>>>>>>>>>>>>>> rejected and not allowed to be used in any logical 
>>>>>>>>>>>>>>>> operations. It
>>>>>>>>>>>>>>>> is basically invalid input.
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> You cannot teach because you lack necessary skills. 
>>>>>>>>>>>>>>> Therefore you
>>>>>>>>>>>>>>> don't need any teaching device.
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> That is too close to ad homimen.
>>>>>>>>>>>>>> If you think my reasoning is incorrect then point to the 
>>>>>>>>>>>>>> error
>>>>>>>>>>>>>> in my reasoning. Saying that in your opinion I am a bad 
>>>>>>>>>>>>>> teacher
>>>>>>>>>>>>>> is too close to ad hominem because it refers to your 
>>>>>>>>>>>>>> opinion of
>>>>>>>>>>>>>> me and utterly bypasses any of my reasoning.
>>>>>>>>>>>>>
>>>>>>>>>>>>> No, it isn't. You introduced youtself as a topic of 
>>>>>>>>>>>>> discussion so
>>>>>>>>>>>>> you are a legitimate topic of discussion.
>>>>>>>>>>>>>
>>>>>>>>>>>>> I didn't claim that there be any reasoning, incorrect or 
>>>>>>>>>>>>> otherwise.
>>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>> If you claim I am a bad teacher you must point out what is 
>>>>>>>>>>>> wrong with
>>>>>>>>>>>> the lesson otherwise your claim that I am a bad teacher is 
>>>>>>>>>>>> essentially
>>>>>>>>>>>> an as hominem attack.
>>>>>>>>>>>
>>>>>>>>>>> You are not a teacher, bad or otherwise. That you lack skills 
>>>>>>>>>>> that
>>>>>>>>>>> happen to be necessary for teaching is obvious from you postings
>>>>>>>>>>> here. A teacher needs to understand human psychology but you 
>>>>>>>>>>> don't.
>>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> You may be correct that I am a terrible teacher.
>>>>>>>>>> None-the-less Mathematicians might not have very much 
>>>>>>>>>> understanding
>>>>>>>>>> of the link between proof theory and computability.
>>>>>>>>>
>>>>>>>>> Sume mathematicians do have very much understanding of that. 
>>>>>>>>> But that
>>>>>>>>> link is not needed for understanding and solving problems 
>>>>>>>>> separately
>>>>>>>>> in the two areas.
>>>>>>>>>
>>>>>>>>>> When I refer to rejecting an invalid input math would seem to 
>>>>>>>>>> construe
>>>>>>>>>> this as nonsense, where as computability theory would totally 
>>>>>>>>>> understand.
>>>>>>>>>
>>>>>>>>> People working on computability theory do not understand 
>>>>>>>>> "invalid input"
>>>>>>>>> as "impossible input".
>>>>>>>>
>>>>>>>> The proof then shows, for any program f that might determine 
>>>>>>>> whether
>>>>>>>> programs halt, that a "pathological" program g, called with some 
>>>>>>>> input,
>>>>>>>> can pass its own source and its input to f and then specifically 
>>>>>>>> do the
>>>>>>>> opposite of what f predicts g will do. No f can exist that 
>>>>>>>> handles this
>>>>>>>> case, thus showing undecidability.
>>>>>>>> https://en.wikipedia.org/wiki/Halting_problem#
>>>>>>>>
>>>>>>>> So then they must believe that there exists an H that does 
>>>>>>>> correctly
>>>>>>>> determine the halt status of every input, some inputs are simply
>>>>>>>> more difficult than others, no inputs are impossible.
>>>>>>>
>>>>>>> That "must" is false as it does not follow from anything.
>>>>>>>
>>>>>>
>>>>>> Sure it does. If there are no "impossible" inputs that entails
>>>>>> that all inputs are possible. When all inputs are possible then
>>>>>> the halting problem proof is wrong.
>>>>>>
>>>>>> *Termination Analyzer H is Not Fooled by Pathological Input D*
>>>>>> https://www.researchgate.net/publication/369971402_Termination_Analyzer_H_is_Not_Fooled_by_Pathological_Input_D
>>>>>>
>>>>>> Everyone that objects to the statement that H(D,D) correctly 
>>>>>> determines the halt status of its inputs say that believe that 
>>>>>> H(D,D) must report on the behavior of the D(D) that invokes H(D,D).
>>>>>
>>>>> Right, because that IS the definition of a Halt Decider.
>>>>>
>>>>
>>>> Everyone here takes the definition of a halt decider to be
>>>> required to determine the halt status of the program that
>>>> invokes this halt decider, knowing full well that the program
>>>> that invokes this halt decider IS NOT ITS INPUT.
>>>>
>>>> All these same people also know the computable functions only
>>>> operate on their inputs and are not allowed to consider anything
>>>> else.
>>>>
>>>> Computable functions are the formalized analogue of the intuitive 
>>>> notion
>>>> of algorithms, in the sense that a function is computable if there
>>>> exists an algorithm that can do the job of the function, i.e. given an
>>>> input of the function domain it can return the corresponding output.
>>>> https://en.wikipedia.org/wiki/Computable_function
>>>>
>>>> When the definition of a halt decider contradicts the definition of
>>>> a computable function they can't both be right.
>>>
>>> When the definitions of a term contradicts the definition of another 
>>> term
>>> then both of them are wrong. A correct definition does not contradict
>>> anything other than a different definition of the same term.
>>>
>>
>> *Wrong*
> 
> That "Wrong" is wrong as it refers to a true statement.
> 
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